few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Topic options: 
A. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
D. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
E. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
F. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
G. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
K. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.


Thought: This problem teaches students different ways of writing numbers that express the same value. This helps students better understand the complex number system, which includes rational numbers.
Answer: I

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001097

7
options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
problem_activity: Narrative
In this activity, students learn how to use a protractor. They align a protractor to the vertex and a ray of an angle so that its measurement can be read. The given angles are oriented in different ways, drawing students’ attention to the two sets of scales on a protractor. Students need to consider which set of numbers to pay attention to and think about a possible explanation for when or how to use each scale. Moreover, one of the scales is only marked in increments of 10 degrees so if students use this scale they need to reason carefully about the precise angle measure (MP6).
This activity uses
MLR1 Stronger and Clearer Each Time. Advances: reading, writing.
Action and Expression: Internalize Executive Functions.
Invite students to estimate the size of the angle before finding each precise measurement. Offer the sentence frame: “This angle will be greater than _____ and less than _____. It will be closer to _____.”
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention
Launch
Groups of 2–4
Activity
5 minutes: independent work time
2–3 minutes: group discussion
Monitor for students who find each measurement by:
looking for the scale with a ray on
\(0^\circ\)
and counting up on that scale
subtracting the two numbers (on the same scale) that the rays pass through
MLR1 Stronger and Clearer Each Time
“Share your response to the last problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: partner discussion
Repeat with 2–3 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Student Facing
Here are four angles whose sizes you may have estimated earlier. A protractor has been placed over each angle. Measure the size of each angle in degrees.
[IMG]
[IMG]
[IMG]
[IMG]
Elena and Kiran are measuring an angle with a protractor. Elena says the angle is
\(80^\circ\)
. Kiran says it shows
\(100^\circ\)
. Why might they end up with different measurements? Which one is correct? Explain your reasoning.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select students who used different strategies to share their responses and reasoning.
Display the image of Elena and Kiran’s angle. If no students mentioned that
\(80^\circ\)
is not possible because the angle clearly appears greater than a right angle (
\(90^\circ\)
), consider asking how Elena can use what she knows about right angles to think about her measurement.


correct_option_index: 6